`text{tìm số nguyên x , y}` `x^2 + 4x + 4 - 9y^2 = 7`

Ta có: `x^2 + 4x + 4 - 9y^2 = 7`

`<=> (x+2)^2 - (3y)^2 = 7`

`<=> (x+2-3y)(x+2+3y) = 7 `

`=> x+2-3y ; x+2+3y` là `Ư(7)`

Ta có bảng sau:

\begin{array}{|c|c|c|}\hline \text{x+2-3y}&\text{1}&\text{-1}&\text{7}&\text{-7}\\\hline \text{x+2+3y}&\text{7}&\text{-7}&\text{1}&\text{-1}\\\hline \text{x-3y}&\text{-1}&\text{-3}&\text{5}&\text{-9}\\\hline \text{x+3y}&\text{5}&\text{-9}&\text{-1}&\text{-3}\\\hline \text{x}&\text{2}&\text{-6}&\text{2}&\text{-6}\\\hline \text{y}&\text{1}&\text{-1}&\text{-1}&\text{1}\\\hline\end{array}

Vậy `(x,y) ∈ {(2,1) ; (-6,-1) ; (2,-1) ; (-6,1)}`